Problem: $ \left(\dfrac{49}{100}\right)^{-\frac{1}{2}}$
$= \left(\dfrac{100}{49}\right)^{\frac{1}{2}}$ Figure out what goes in the blank: $\Big(? \Big)^{2}=\dfrac{100}{49}$ Figure out what goes in the blank: $\Big({\dfrac{10}{7}}\Big)^{2}=\dfrac{100}{49}$ So $\left(\dfrac{49}{100}\right)^{-\frac{1}{2}}=\left(\dfrac{100}{49}\right)^{\frac{1}{2}}=\dfrac{10}{7}$